What are the zeroes and asymptotes of (2x)/(x^2-4) ?

Question

please help !

Answer 1

Asymptotes of (2x) / (x^2 - 4)

Vertical asymptotes at 2 , -2

Given that x^2 - 4 = 0

Add 4 to each side

x^2 - 4 + 4 = 4

x^2 + 0 = 4

x^2 = 4

Take square root  to each side

x = +2 , -2.

Horizontal asymptote :

Horizontal asymptote  at 2 is  2x / x = 2

Zeros :

2x = 0

Divide each side by 2

x = 0.

 

Answer 2

The rational function

Vertical asymptotes are found  by solving denominator = 0

Vertical asymptotes are

To find horizontal asymptote.

Degree of the numarator = 1 and the degree of denominator = 2.

If the degree of the numerator is less than the degree of the denominator, the line y = 0 (x - axis) is the horizontal asymptote.

To find zeros of function

Zeros of the function is x  intercept and y  intercept.

To find y  intercept substitute x  = 0 in the function.

To find x  intercept substitute y  = 0 in the function.

Zeros are x  = 0 and y  = 0.